OF MOLECULAR FORCES. 101 



hyperboloids of one and two sheets, the common centre of which is the 

 point of neutral attraction. Certain points, however, have the asymptotic 

 surface for their characteristic surface. 



Let fgh be the co-ordinates of K, the point of neutral attraction, 

 and f + x, g + y, h + «, the co-ordinates of P, a point very near to 

 K. Let the value of V at K be C, and at P, C. Then the equa- 

 tions to the respective surfaces are 



C = V, and C = V ; 

 where V is the same function of / + x, g + y, k + « that V is of f 



.: C= V + d f V.x + d a V.y + d h V.x + d}V .^ + d 2 g V .% 



as 2 

 + d\V .- + d f d g V ,xy + dfd h V .x% + d g d h V ,y% + &c. 

 SB 



But because K is a point of neutral attraction, d f V = 0, d g V = 0, 

 d h V=0, and 



.-. 2(C- C) = d}F.x* + dlF.y* + dlV.%* + 2d,d g U.xy + &c. 



This, neglecting terms above the second order, being the general 

 equation of surfaces of the second order which have a centre, by 

 transposing the co-ordinate axes so as to coincide with the principal 

 axes of the surface, the terms containing xy, y%, x» will disappear, 

 leaving only 



2(C- C) = d* f V.x* + d g V.tf + d\V.%\ 



which for indefinitely small values of x, y, % may be regarded as the 

 equation of the parametric surface. It must be remembered that the 

 coefficients of a?, if, ss s are subject to the condition, 



= d}r+d g F+dlV; 



and because at least one of these coefficients will be negative, and one 

 positive, the equation is that of an hyperboloid. 



